The phase of a signal provides valuable information that may be useful in several applications. For example, the phase of a wireless communication signal as it is received at multiple antennas may be used to determine an angle of arrival of the wireless communication signal, which indicates a direction from which the wireless communication signal was transmitted relative to a receiver. Conventional systems and methods for measuring the phase of a wireless communication signal rely on a highly linear receiver. However, highly linear receivers are costly both monetarily and in terms of power consumption. Accordingly, phase measurement and thus angle of arrival estimation has been unavailable for low-cost and low-power applications such as Internet of Things (IoT) devices. In light of the above, there is a need for systems and methods for measuring the phase of a wireless receive signal that are suited to non-linear (e.g., hard limiting) receiver architectures.